Greedy adaptive walks on a correlated fitness landscape

Abstract

We study adaptation of a haploid asexual population on a fitness landscape defined over binary genotype sequences of length L. We consider greedy adaptive walks in which the population moves to the fittest among all single mutant neighbors of the current genotype until a local fitness maximum is reached. The landscape is of the rough mount Fuji type, which means that the fitness value assigned to a sequence is the sum of a random and a deterministic component. The random components are independent and identically distributed random variables, and the deterministic component varies linearly with the distance to a reference sequence. The deterministic fitness gradient c is a parameter that interpolates between the limits of an uncorrelated random landscape (c = 0) and an effectively additive landscape (c → ∞). When the random fitness component is chosen from the Gumbel distribution, explicit expressions for the distribution of the number of steps taken by the greedy walk are obtained, and it is shown that the walk length varies non-monotonically with the strength of the fitness gradient when the starting point is sufficiently close to the reference sequence. Asymptotic results for general distributions of the random fitness component are obtained using extreme value theory, and it is found that the walk length attains a non-trivial limit for L → ∞, different from its values for c = 0 and c = ∞, if c is scaled with L in an appropriate combination.

Selection Limits to Adaptive Walks on Correlated Landscapes

“…Under this reasoning, the “easiest” landscape would be one where each locus contributes equally and independently to fitness, such as in the present manuscript. Indeed, this is the case for hill climbers in which mutations are deterministically accepted or rejected based on whether they increase or decrease fitness ( Droste 2002 ), regardless of the magnitude of their effect (random adaptive walks), or in which the best available mutation is always accepted (greedy hill climbers) ( Macken and Perelsont 1989 ; Park et al 2016 ). However, such adaptive walks may not be adequate models of natural adaptation, except perhaps when the fitness effects of all mutations are extremely large.…”

“…Other studies have focused on the properties of adaptive walks, which explicitly consider the discrete nature of the genotype space ( Kauffman and Levin 1987 ; Orr 2002 ; Park et al 2016 ). Many of these studies have focused on models of fitness landscapes that can display high levels of ruggedness, such as the house-of-cards model ( Kingman 1978 ), in which fitness values are drawn randomly from some distribution; the rough Mount Fuji ( Aita et al 2000 ), in which fitness effects , combined with a deterministic part of fitness, are drawn randomly; or the NK model, in which the fitness effect of a locus depends, in some randomly prescribed way, on the state of K other loci ( Kauffman and Weinberger 1989 ).…”

Adaptive walks on high-dimensional fitness landscapes and seascapes with distance-dependent statistics

“…There have been several recent numerical studies analyzing adaptive walks in the simpler NK and RMF models [40,42,45,46]. These works have primarily focused on the lengths of adaptive walks before a local maximum is reached.…”

“…Models should have no "special genomes" -such as "wild-type" -a priori, and instead one should carry out evolution from a random point and then try to understand the effects of epistasis and further evolution conditioned on past evolution. Some recent work has endeavored to analyze evolutionary dynamics on some classes of landscapes with simple models of epistasis, [25,40,42,45,46]; however these analyses are computationally limited from exploring more general, or more high-dimensional landscapes.…”

Analysis of statistical correlations between properties of adaptive walks in fitness landscapes

“…open sci. 7: 192118 landscapes unveil that the topography of the landscape plays a role, usually resulting in longer walk lengths when compared to the uncorrelated case but this cannot be stated as a general rule [26,33,34]. The dependence of the adaptive walk length on the initial fitness has also been addressed.…”